Today it seems that O2 has identified the issue and is working on a fix: "We are aware of an issue currently impacting data access for some of our customers," they told Sky News Online. "We have identified a fault with the allocation of IP addresses and are working to resolve this as quickly as possible. We apologise to any affected customers."
Some Twitter users have noted a return of service, while others wait. We've got our fingers crossed for you all. Good luck!